Detecting transverse cracks initiation in composite laminates via statistical analysis of sensitivity data

Highlights

• The sensitivity of the stress response in a transverse ply with respect to individual fiber/matrix interface strengths provides a method to predict crack initiation.

• A rapid departure of the distribution of sensitivity data from a specific distribution can pinpoint cracks initiation to formation strain levels.

• The prediction of cracks initiation can be used to increase the reliability of laminates’ designs.

Abstract

This study presents a novel method to describe the microscale phenomenon of cracks initiation based on sensitivity analysis in laminate fiber-reinforced composites. The failure of fiber-reinforced composite laminates often roots in the microscale phenomenon of fiber/matrix interfacial debonding. The micro-cracking and interfacial debonding in composites are difficult to detect both experimentally and numerically. This paper shows that the sensitivity of the stress response in a transverse ply with respect to individual fiber/matrix interface cohesive properties follows a normal distribution before cracks initiate. The distribution of the sensitivities rapidly deviates from a normal distribution from crack initiation to the formation. Several realistic microstructural representations of a fiber-reinforced composite laminate are simulated to validate the proposed method of detecting crack initiation. This proposed prediction method of crack initiation can be used as a failure risk indicator to increase the reliability of laminates’ designs.

Introduction

In laminate fiber-reinforced composites, cracks initiate around the fibers aligned transversely to the loading direction [1]. The transverse cracks initiated at the microscale then propagate within the laminate ply and induce the sequential accumulation of damage. The transverse cracks can potentially cause leakage in specific applications, or progress to inter-ply delamination and catastrophic failure [2], [3], [4]. Initiated micro-cracks can go undetected since theinstantaneousloss in the composites’ response is negligible [5]. Current experimental and numerical works can mainly predict the macroscopic phenomenon of cracks formation and fall short of giving insight into the microscopic event of cracks initiation. The stochastic variations in the microstructural properties further complicate the prediction of the start of cracks in composite laminates. The risk of undetected microcracking, in addition to variabilities in the microstructure, causes a high level of uncertainty and therefore significant safety factors in the composites’ design [6]. Hence, an accurate estimation of the initiation of transverse cracking is imperative to improve the reliability of laminate composites design and utilization.

The present study provides insight into the microscale phenomenon of crack initiation by developing a novel method to predict the applied strain level at which interfaces start to debond. It was previously shown that sensitivity of the macroscopic response of the fiber-reinforced composites to individual fiber/matrix interface properties can be easily calculated at each step of loading in the numerical simulations [7]. It is herein argued that the set of computed sensitivities contains information about crack initiation. Before the cracks initiate, the sensitivities depend on many local factors and can be well described by a suitably scaled normal distribution. As soon as cracks initiate, the stress response within the microstructure changes, driving abrupt departure from normality in the distribution of sensitivities. This simple idea is illustrated with simulation results in Fig. 1. Here the departure from normality is measured using the Kolmogorov–Smirnov (KS) statistic¹ of the sensitivity data, which is plotted versus the applied strain. For comparison, the percentages of failing and failed cohesive interfaces (see Section 4.1 for their quantitative definition) are also plotted. These percentages also indicate the initiation and formation of cracks but are much more difficult to compute than the sensitivities.

It is evident from Fig. 1 that the interval from crack initiation to formation coincides with the most rapid growth in the KS statistic. It should be emphasized that the point of crack initiation (${ϵ}_{app}=0.0145$ in the figure) cannot be detected in the transverse stress-strain responses presented in Fig. 2. It is also not discernible in the visual inspection of the stress response contours shown in Fig. 3(a). Thus, it is argued that the distribution of sensitivities (or, quantitatively, its distance from a normal distribution) can be used as a more precise breakage risk indicator, providing valuable microscale information without detailed and expensive microstructural investigations.This prediction of crack initiation is the contribution of this work, and to the best knowledge of the author, there is no other method that tackles this specific issue.

Different finite element based methods were developed to simulate the responses of composite laminates at the microscale. The numerical methods can be used to track the fiber/matrix debonding, and therefore, the location and strain level at which micro-cracks initiate [8], [9]. However, tracking debonding in all interfacial nodes during the loading history is computationally very expensive.Methodologies to determine the sensitivity of the composites’ macroscopic behavior, such as transverse stress, to the local characteristics, such as material parameters of constituents, were also developed [8], [10], [11], [12], [13]. However, to the best of our knowledge, no study used the sensitivity of the macroscopic stress response to determine when and where micro-cracks initiate and propagate. Thus, this paperemphasizes the physical significance of the sensitivities and how the distribution of sensitivities can be used to predict the cracks initiation. The developed approach herein uses the sensitivity results in a novel way to distinguish the critical phenomenon of crack initiation.